Abstarct: Process capability indices are used to determine whether a production process is capable of producing items within specification tolerance. they are very useful statistical tools to summarize process dispersion and location by using process capability analysis. However, there are some limitations which prevent a deep and flexible analysis shuch as the crisp definition of quality and precise definition of data. in this thesis, a flexible generation of PCIs is proposed which is able to measure the process capability baxsed on fuzzy quality and fuzzy data. ‎Therefore, introducing and considering fuzzy specification limits can minimize the number of non-conform items and so decrease the product costs. The major motivation for introducing two special kinds of linear and exponential fuzzy specification limits, and also considering two special kinds of triangular fuzzy number and normal fuzzy number, is obtaining some fast computing formulas for the estimations of the process capability indices. ‎In this thesis several approaches to obtaining approximate confidence intervals for the PCIs in a bootstrap. the methods include "the standard normal bootstrap confidence interval, "the basic bootstrap confidence interval", "the percentile bootstrap confidence interval, "the bootstrap t confidence interval" and "the bootstrap bias corrected acceleration". A practical example is presented to show the performance of proposed indices and bootstrap confidence interval of them.‎